Minimum Perimeter-Sum Partitions in the Plane
Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P_1 and P_2 such that the sum of the perimeters of CH(P_1) and CH(P_2) is minimized, where CH(P_i) denotes the convex hull of P_i. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n^2) time algorithm. Despite considerable progress on related problems, no subquadratic time algorithm for this problem was found so far. We present an exact algorithm solving the problem in O(n log^4 n) time and a (1+e)-approximation algorithm running in O(n + 1/e^2 log^4(1/e)) time.
Computational geometry
clustering
minimum-perimeter partition
convex hull
4:1-4:15
Regular Paper
Mikkel
Abrahamsen
Mikkel Abrahamsen
Mark
de Berg
Mark de Berg
Kevin
Buchin
Kevin Buchin
Mehran
Mehr
Mehran Mehr
Ali D.
Mehrabi
Ali D. Mehrabi
10.4230/LIPIcs.SoCG.2017.4
Creative Commons Attribution 3.0 Unported license
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